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A176537
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Decimal expansion of 5 + sqrt(26).
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5
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1, 0, 0, 9, 9, 0, 1, 9, 5, 1, 3, 5, 9, 2, 7, 8, 4, 8, 3, 0, 0, 2, 8, 2, 2, 4, 1, 0, 9, 0, 2, 2, 7, 8, 1, 9, 8, 9, 5, 6, 3, 7, 7, 0, 9, 4, 6, 0, 9, 9, 5, 9, 6, 4, 0, 7, 5, 8, 4, 9, 7, 0, 8, 0, 4, 4, 2, 5, 9, 3, 3, 6, 3, 2, 0, 6, 2, 2, 2, 4, 1, 9, 5, 5, 8, 8, 3, 4, 8, 8, 5, 1, 0, 9, 3, 9, 3, 2, 0, 0, 8, 3, 6, 1, 1
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OFFSET
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2,4
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COMMENTS
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Continued fraction expansion of 5 + sqrt(26) is A010692.
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LINKS
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FORMULA
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Equals exp(arcsinh(5)), since arcsinh(x) = log(x + sqrt(x^2 + 1)). - Stanislav Sykora, Nov 01 2013
Equals limit_{n->infinity} S(n, 2*sqrt(2*13))/ S(n-1, 2*sqrt(2*13)), with the S-Chebyshev polynomilas (see A049310). - Wolfdieter Lang, Nov 15 2023
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EXAMPLE
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5+sqrt(26) = 10.09901951359278483002...
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MATHEMATICA
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r=10; t = (r + (4+r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
RealDigits[5+Sqrt[26], 10, 120][[1]] (* Harvey P. Dale, Jun 24 2013 *)
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PROG
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CROSSREFS
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Cf. A010481 (decimal expansion of sqrt(26)), A010692 (all 10's sequence).
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KEYWORD
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AUTHOR
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STATUS
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approved
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